Constraints on neutrino masses from leptogenesis models

Upper bounds on the CP asymmetry relevant for leptogenesis are reexamined and found weaker than in previous literature, both for hierarchical and for quasi-degenerate righthanded neutrinos. Successful leptogenesis implies the usual lower bound on right-handed neutrino masses, and an upper bound on left-handed neutrino masses (which we obtain to be 0.15 eV at 3σ) only if right-handed neutrinos are assumed to be much more hierarchical than left-handed neutrinos. Otherwise both bounds can be considerably relaxed. The constraint on light neutrino masses varies assuming different interpretations of why neutrinos should be quasi-degenerate. With conservative assumptions, we find that a mild quasi-degeneracy allows neutrinos heavier than an eV compatibly with leptogenesis. We also extend computations of thermal leptogenesis to an alternative model of neutrino mass mediated by fermion triplets which was never considered so far for leptogenesis. Leptogenesis can be successful despite the effect of gauge interactions, resulting in only slightly stronger constraints on neutrino masses. Assuming that neutrino masses are generated by tree level exchange of right-handed neutrinos, that the observed baryon asymmetry is produced via thermal leptogenesis [1] and that right-handed neutrinos are hierarchical, one can derive interesting constraints [2, 3, 4]: right-handed neutrinos must be heavier than about 108 GeV and left-handed neutrinos must be lighter than about 0.1 eV [3, 4]. Since the former constraint leads to a possible conflict between leptogenesis and gravitino overproduction, and since the later one is stronger than present experimental bounds and is close to the mass scale suggested by atmospheric oscillations (i.e. m3 >∼ 0.05 eV), in this article we reconsider these constraints in details. To this end we adopt the results of [4] for a precise computation of the dynamics of thermal leptogenesis, and we reexamine the upper bound on CP violation in right-handed neutrino decays. In section 1 we consider a hierarchical spectrum of right-handed neutrinos. We show that the lower bound above on their masses can be significantly evaded dropping the assumption (made in [2]) that the hierarchy among right-handed neutrinos is much larger than the observed one among lefthanded neutrinos. Moreover, even under this assumption, we derive a precise upper bound on the CP-asymmetry and find it weaker than in previous literature [3], leading to a slightly higher neutrino mass bound. Since this constraint is based on the doubtful assumption that quasi-degenerate neutrinos be produced by hierarchical right-handed neutrinos, in section 2 we study what happens allowing quasidegenerate right-handed neutrinos. As well known, the asymmetry can be resonantly enhanced [5, 6]; with respect to the analysis of [3] we find other effects that relax the upper bound on the CP-asymmetry so that our constraint on neutrino masses is much weaker. We discuss how the result depends on possible reasons that naturally give rise to quasi-degenerate left-handed neutrinos.